Computer Aided Design method for enhancement of local refinement trough T-Splines

ABSTRACT

One embodiment of the present technology provides a the method comprises the steps of: Converting B-spline networks to T-splines, Converting NURBS into T-spline surfaces, Adding control points to local regions, Scaling or optimizing weights across the mesh, and merging between NURBS and T-spline surfaces. The technology overcame some of the issues with implementing simultaneous multiple surface design methodology when dealing with groups of lenses and reflectors, by improving seed patch junction continuity, elimination of ripples and holes, and precisely adding control points where required. In at least one embodiment of the technology, the t-splines topology allowed for refined control over the optical surface. Control points were reduced by conversion of a NURBS into a T-spline. T-splines were used to produce new loft lenses which were further refined and merged to spline patches. In another embodiment of the present technology, the T-spline loft lens network was subsequently optimized through reverse raytracing, bi-directional raytracing, flow-line, optical path, or flux tube approach.

CROSS REFERENCE TO RELATED APPLICATION

This application is a non-provisional application which claims thebenefit of priority under 35 U.S.C Section 119 from U.S. provisionalapplication “BEYOND NURBS: ENHANCEMENT OF LOCAL REFINEMENT THROUGHT-SPLINES” No. 60/979,498 filed Oct. 12, 2007.

FIELD OF THE TECHNOLOGY

The disclosure relates to the art of Computer Aided Graphic Design, inparticular to Non-Uniform Rational B-Splines, T-splines and T-NURCC infree-form design, in order to accelerate local refinement by simplifyingcontrol point addition allowing the CAD designer to increase controlsurface detail where needed.

BACKGROUND OF THE TECHNOLOGY

The optical design community has progressed in parallel with theadvancements of computer aided design (CAD) and computer aided geometrydesign (CAGD) for many years. As computer aided design has progressedfrom simple curves, conics, and aspheric polynomials the applicationshave transitioned to optical design shortly thereafter or in parallel.Many problems in computer aided design allow for error many orders ofmagnitude higher than those tolerances allowed in optical design. Theoptical design community following its own relentless pursuit ofdiffraction limited performance and has pushed transversely to improvecomputer aided design to higher levels of precision. Gradually, moredifficult optical problems have required creativity to push computeraided design further into the realm of optical design code. There aretypically resistances to do so as the mathematics concerning simplecurves, and aspherics, the associated wavefronts and aberrations is wellunderstood. Metrology to inspect such advanced geometries also has tocome up to speed in parallel, otherwise design realized on the computercannot be verified with empirical data to ensure that what was designedwas indeed manufactured precisely.

Many designers were the most resistant to embracing the computer-aideddesign world largely due to limitations in the free-form design space.The entertainment and defense industries with vast monetary resourceshas pushed the realization of more general design tools to the computerdesign space. The parametric mathematics has progressed from Bernsteinpolynomials, to Bezier curves, B-splines, and then tensor productsurfaces or NURBS (Non-Uniform Rational B-Splines). Computer aidedgeometry design today is largely dominated by NURBS and sub-divisionsurface modeling. In an effort to advance local refinement and free-formdeformation T-splines are introduced as a new generalization of NURBS.To fully appreciate the advancement it is necessary to compilecomparisons between the two topologies, the mechanics ofknot-insertion/deletion, and how the non-imaging and imaging communitymay become beneficiaries of the application.

In the optical design arts for example, it would be desirable toprogress from simple spherical control surfaces to conics and asphericsbefore entering the t-spline lens space. In some applications a meritfunction can be achieved with sequences of simple spherical surfaces. Inmany non-imaging applications which require tailoring the lightemanating from an extended source spherical surfaces offer insufficientoptical control. Progressing to a NURBS surface or spline patch gridsurface presents challenges.

Control of the light at a local control point can be performed byiterative Cartesian oval calculations, but it is a tedious process withso many superfluous control points in close proximity to a local surfacechange. If one desires to add control perturbation to a sectionin-between the surface spline control points knot insertion producesexponentially greater complexity. Trying to add one knot at an opticalcontrol surface section of interest requires adding an entire row ofcontrol points to satisfy the rectangular NURBS grid topology.

One way to locally refine is to trim the NURBS with a cutting surfaceand then add control points. Joining additional surfaces to the trimmedNURBS becomes a problem and rips can frequently occur. For some modelsthe rips and discontinuities at a NURBS junction can be ignored due tocoarse machine tolerances. Rips and gaps however, produce problems forefficient and accurate optical raytracing, requiring post-processhealing, and iterative surface approximation routines. These rips aremore likely to occur when attempting to merge bezier edge curves withdissimilar continuity.

For the foregoing reasons, there is a need in the optical designindustry to develop a method to refine geometries without the additionof superfluous control points.

There is also a further need to develop a method for interoperabilitybetween NURBS and T-splines surfaces for optical design that willaccelerate adaptation allowing for compatibility with opto-mechanicalsoftware, tooling, and manufacturing.

BRIEF SUMMARY OF THE TECHNOLOGY

The present technology provides a method for tensor product surfacelocal refinement through T-spline networks for CAD designs.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

The foregoing summary, as well as the following detailed description ofthe technology, will be better understood when read in conjunction withthe appended drawings. For the purpose of illustrating the technology,there are shown in the embodiments which are presently preferred. Itshould be understood, however, that the technology is not limited to theprecise arrangements and instrumentalities shown. In the drawings:

FIG. 1 depicts a NURBS surface described with (117) one hundredseventeen control points increases to (156) one hundred fifty-six withthe addition of only three knots which constitutes a 33% increase.

FIG. 2 depicts a “rip” shown at the junction of two trimmed NURBS.

FIG. 3 depicts a T-spline control grid or control point lattice, withT-junctions and a T-spline surface.

FIG. 4 depicts a NURBS surface with a rectangular control point mesh.

FIG. 5 depicts an embodiment of the technology, where a B-spline networkis converted to a NURBS surface.

FIG. 6 depicts an embodiment of the technology, where NURBS network isconverted to T-spline network.

FIG. 7 depicts an embodiment of the technology, with a T-spline networkrepresentation comprised of only (35) thirty five starting controlpoints. Beginning with only the essential control points allows forlocal knot insertion at important areas.

FIG. 8 depicts an embodiment of the technology, where the equivalentgeometry of FIG. 7 in a NURBS surface requires (154) one hundred fiftyfour control points.

FIG. 9 depicts an embodiment of the technology, where a “rip”-free mergewas produced between dissimilar NURBS to T-spline loft lensparameterizations.

FIG. 10 depicts an embodiment of the technology, where a T-splineoptical control surface was produced from a curve network and itsequivalent T-spline optical control surface with a total of (35)thirty-five control points.

FIG. 11 depicts a method of the technology for tensor product surfaceinterpolation of NURBS and T-splines networks.

FIG. 12 depicts an embodiment of the technology, where a T-spline lenscontrols the refraction of the light rays, in which the rays representthe wavefront of light.

FIG. 13 depicts an embodiment of the technology, where a T-spline lightcontrol lens operates upon the light in 3D in which the lens iscomprised of T-panels or T-junction local light refinement surfaces.

DESCRIPTION OF THE TECHNOLOGY

It shall be understood to the person skilled in the art that “NURBS”refers to Non-uniform rational B-spline which is a mathematical modelused in computer graphics for generating and representing curves andsurfaces. B-splines are a way of defining a group of degree n Beziercurves that works irrespective of control point location and joins withĈ(n−1) continuity. The formula describing the Bezier curve is:

${P(t)} = {\sum\limits_{i = 0}^{n}\; {\begin{pmatrix}n \\i\end{pmatrix}\left( {1 - t} \right)^{n - i}t^{i}P_{i}}}$

The formulation of the Bezier curve equation consists of the ithBernstein polynomial up to degree n in which the parametric variable tstitches the space between the points P_(i). B-splines such as in 510have local control as inserting a knot only requires updating the fewnearby control points of the n degree curve segments. Families ofB-splines 510 form NURBS surfaces 120.

It shall be further understood to the person skilled in the art thattensor product surfaces are formulated from B-spline or Bezier blendingfunctions and include control points and weights:

${P\left( {s,t} \right)} = \frac{\sum\limits_{i = 0}^{m}\; {\sum\limits_{j = 0}^{n}\; {w_{ij}P_{ij}{B_{i}^{m}(s)}{B_{j}^{n}(t)}}}}{\sum\limits_{i = 0}^{m}\; {\sum\limits_{j = 0}^{n}{w_{ij}{B_{i}^{m}(s)}{B_{j}^{n}(t)}}}}$

Knot insertion is difficult for a tensor product B-spline surfacebecause adding one knot 130 requires adding an entire column or row ofcontrol points 110 as shown in FIG. 1. Local refinement through knot 130insertion is possible through Boehm's algorithm which operates on theB-spline coefficients, by the Oslo algorithm which computes subspacediscrete B-splines, and through the blossoming principle devised byGoldman. On the other hand, knot 130 removal is not always possiblewithout disrupting the geometry. Knot 130 removal without disruption canonly occur when the two adjacent curve segments are at a continuitylevel greater than the difference between the curve degree andmultiplicity of the knot.

As depicted in FIG. 3 T-spline control grids 310 or control pointlattice 310, permit T-junctions 340, so lines of control points 110 neednot traverse the entire control grid as seen in FIG. 4. T-splinessupport many valuable operations within a consistent framework, such aslocal refinement, and the merging of several B-spline surfaces that havedifferent knot vectors into a single gap-free model. A T-spline surface320 which is comprised of a control point lattice 310 is also called aT-mesh 310. In the optical design arts, a control point lattice 310becomes an optical control surface 720.

A T-spline optical control surface such as the one in FIG. 7 can bedescribed as follows:

${P\left( {s,t} \right)} = {\left( {{x\left( {s,t} \right)},{y\left( {s,t} \right)},{z\left( {s,t} \right)},{w\left( {s,t} \right)}} \right) = {\sum\limits_{i = 1}^{n}\; {P_{i}{B_{i}\left( {s,t} \right)}}}}$

in which a T-spline mesh consists of a group of control points 110, theweights of the points, a T-mesh 310, and a neighborhood or network ofpoints 330 on the T-spline surface 320. The coordinates of such points110 and 330 in Cartesian space are defined as:

$\frac{\sum\limits_{i = 1}^{n}{\left( {x_{i},y_{i},z_{i}} \right){B_{i}\left( {s,t} \right)}}}{\sum\limits_{i = 1}^{n}{w_{i}{B_{i}\left( {s,t} \right)}}}$

The blending function Bi(s,t) is given by N[si0,si1,si2,si3,si4](s)N[ti0, ti1, ti2, ti3, ti4](t) where N[si1 . . . 4](s) is the B-splinebasis function for the knot vector: si=[si0 . . . 4] and N[ti0 . . .4](t) is defined by the knot vector ti=[ti0 . . . 4].

In the optical design and computer modeling arts, the limitation withNURBS in FIG. 1 is that the location of the control point is likely notwhere the bad skew ray has passed, and a change to the control point maydisturb the rays propagating in the correct directions. A lightwavefront containing many skew rays produces local caustics duringpropagation and is historically difficult to control. T-splines of FIG.3 and as applied in FIG. 7, enables the local refinement of the opticalcontrol region where local ray bundles exhibiting undesirable directioncosines are corrected without changing the propagation of the rays withgood behavior.

Another optimization limitation traditionally encountered in the opticaldesigns of lenses, reflectors, and diffractive elements is with regardsto rotational symmetry. For example, an optimizer typically cannottraverse from a symmetric revolved Spline lens or reflector to anon-rotationally symmetric bi-directional polynomial or tensor productNURBS 120 patch network such as in FIG. 1. When converting from aneasily optimizable geometry to a more general topology, it would beadvantageous to lock geometric regions which are well defined in termsof light behavior and where ray direction cosines meet the designrequirements and to add local refinement only to regions exhibitinganomalous ray path behavior 123. T-splines such as in FIG. 12, offer thedissimilar continuity merge of FIG. 9, and local refinement toolsrequired to open up optimization potential as such it can be constituted“enhanced free-form” or EFF as traditional “free-form” designs such asin FIG. 13 are constrained to either subdivisional catmull-clark orNURBS topologies.

The disclosed technology eliminates the aforementioned challenges oflocalized refinement to perturb ray-paths 122 or to design optics as inFIG. 9, FIG. 12 and FIG. 13 with fine structure not attainable withNURBS. The technology uses knot-addition 330, and reverse ray-tracinglocalization. Identifying the light control regions of interest occursin a b-directional manner in which rays are forward raytraced directfrom the source through the light control surfaces to a receiver plane.Receiver mesh regions detecting the highest density of anomalous lightbehavior then becomes a second raytrace source in which the directioncosines are inverted. The localized region on the receiver mesh gridthen propagates rays back towards the light control surface. The lightcontrol surfaces become surface receivers and the local refinementregions are identified which have the highest probability of correctingthe ray behavior. Control knots, points, and weights near the locallight control region are added through the T-spline local refinementtechnique. Forward raytracing then verifies the ray path correction.Additional cycles of forward and reverse raytracing may be necessary tocorrect a light bundle containing complex caustics. The technologyfurther advantageously produces the T-Junction 340 by launching at leastone tangent ray. Yet another advantage of the technology is that itallows an optimizer to progress from simple geometric entities to morecomplex geometry. Traditionally an optical geometry optimizer will onlyoperate on the lens entity prescription chosen. For example, an asphericlens will not convert to an exact B-spline lens replication afterexhausting refinement of the highest order aspheric term.

FIG. 11 depicts at least one preferred method of the disclosedtechnology, it is understood that the order of the elements may vary asthe technology is understood to the person skilled in the art, themethod comprises the steps of: Converting B-spline networks to NURBS112, Converting NURBS into T-spline surfaces 111, Adding Control Pointsto local regions 113, Scaling or Optimizing weights across the mesh 114in terms of flux density or in the alternative the geometry gradient,and merging between NURBS and T-spline surfaces 115. Additionally it isadvantageous to begin with either a B-spline curve network or apowell-sabin spline network and then converting the loft curve networkdirectly to a t-spline surface or solid directly without theintermediate NURBS conversion step.

It should be further understood to the person skilled in the art, thatthe aforementioned process is comprised of a series of steps that areperformed on or with the aid of a computer. The described technologyuses the transformation of data produced by different mediums includingbut not limited to, data input devices such as laser, keyboard, mouse,optical reading, manual input of coordinates, scanning devices, tabletsand sensors. The technology methodology further manipulates the data inthe CAD software which includes but is not limited to B-Splines,T-Splines, T-NURCC, NSS, NURBS, and D-NURBS along with its complementaryalgorithms. The technology further produces at least a useful, concrete,and tangible result which is the modeling of surfaces of at least (1)one dimension.

FIG. 5 depicts one element 112 of the described technology. A B-splinenetwork 510 is converted to NURBS 120, said conversion produces theclassic NURBS rectangular grid topology as shown in 100-B. Theconversion maybe made by at least one, but not limited to the algorithmsdescribed by Boehm, Sablonniere, de Casteljau, Ramshaw; Casciola et aland Prautzsch et al.

FIG. 6 depicts another element 111 of the described technology where aB-Spline curve network 120 is converted to a T-spline network 310. ANURBS mesh 120 can be converted to a T-spline mesh 310 and vice versawithout loss and advantageously precludes knot insertion control pointredundancies such as the ones found in FIG. 1. FIG. 6 depicts at leastone example of bi-directional NURBS/T-spline conversion. This approachwas investigated, and although preferred, is not limited to NURBS andT-Splines, it could also comprise; T-NURCC, NSS, and D-NURBS. Theconversion may be made by at least one, but not limited to thealgorithms described by Sederberg, Zheng, Lyche, Belyaev, and Song etal.

The NURBS was advantageously converted to a T-spline surface 320 toavoid the superfluous NURBS knot insertion depicted in FIG. 1. The totalnumber of control points was reduced in many cases by up to 60%representing the same geometry. Conversion to a T-spline surfaceoccurred at the final stage of optical design where the specificationcannot be met without free-form local control point manipulation. Anadvantage of the disclosed technology is that existing globaloptimization algorithms can operate upon B-spline networks, or B-splinepatch surfaces for the first stage of geometry discovery and thenlocally-refined T-spline surface optimization can finally bring toreality the light control of interest.

After conversion from a NURBS to a T-spline in FIG. 6, control pointswere then added locally 330, element 113, thus overcoming the NURBS rowcontrol point addition problems exhibited in FIG. 1. Yet anotheradvantage of said conversion is to bidirectional pass from NURBS toT-splines, is to advantageously start with a T-spline and then addcontrol points only where needed. 101-A depicts a T-spline opticalcontrol surface 720 produced from a curve network. T-spline opticalcontrol surface 720 has a total of thirty five (35) control points 110in contrast to the equivalent geometry in a NURBS of FIG. 8 thatrequires one hundred fifty four (154) control points. The representationof the same geometry with so many control points gives the falserepresentation of more free-form capability. This is in fact artificialassurance as the location of the control points 110 is constrained tothe NURBS rectangular grid 120. In FIG. 7, a T-spline network embodimentof the present technology uses only thirty five (35) starting controlpoints and allows local knot insertion 330 at the importance area 710.Adding optical control power locally where ray density, or geometrygradients are highest, such as in 123 can affect the most change overthe incoming extended source wavefront.

By advantageously using T-splines, the present technology not onlyreduces redundant control points significantly, but also removes tediousripples 210. These ripples 210 and lack of refined knot 130 placementlimits the performance of NURBS lenses such as the one depicted in900-B. The commonly found wrinkles 210 in the skinned surface patchNURBS 220 can produce problems when implementing traditionalsimultaneous multiple surface or SMS design. Ripple 210 problems occursat the seed patch junctions. As depicted in FIG. 9, a T-Spline Loft Lens720, and a T-spline converted NURBS with different edge parameterization910 are sometimes needed to form a complex geometric lens. Both theT-spline loft lens and a T-spline converted NURBS 900-A are shown beforea rip-free 920 merge operation in 900-B. FIG. 9 depicts how thedisclosed technology is used to merge dissimilar parameterizations suchas 720 and 910. The T-spline loft lens shown in 720 has local opticalcontrol regions as shown at the T-junctions 310. In 910, the T-splineconverted NURBS surface has a different edge parameterization. Arip-free 900-B merge was achieved between two dissimilar continuitieswith minimal superfluous control-point addition.

The optimization element 114 of FIG. 11 was investigated and at leastone preferred method was found by using local refinement through thesplitting and scaling of the b-spline blending functions in theproximity of the local knot vector. This refinement was made possiblebecause at the local regions of the T-spline control point mesh, weightscan be scaled across the mesh in terms of flux density or geometrygradient. As seen in FIG. 13, T-spline optical control surface with rayexit points of interest 123 where control knots are needed for optimumoptical modeling and control. The distinguishing characteristic of theT-spline is in the inferred knot vector determination for producing theblending functions through a reference parameter ray. By scaling theblending functions through iterative knot vector projection allows forthe new t-junction local refinement technique.

Embodiments of the present technology in FIG. 12 and FIG. 13 depictsaccurate raytracing of surfaces that required rapid normal vector searchat the dielectric to air, or reflective interface 101. The rays 102 withtheir associated flux, x,y,z, 131 coordinates, and associated directioncosines are added together as they pass through the receiver grid. Anerror function was produced by analyzing the evaluated ray propertieswith those of the merit function or ideal ray bundle model. In thisembodiment, the rays 102 formulate approximations of the propagation ofthe real light wavefronts. In non-imaging optics the skew rays exiting112 an extended source present a challenge and surfaces must be added inparallel.

The location of the control surface of FIG. 13 was determined byfiltering the 3d line segments of the stray rays of control interest andback-propagating to the exact spatial intersections with the opticalcontrol surface, changing the optical control surface. The opticalcontrol surface can be changed for optimization purposes, but are notlimited to; flow-line method, SMS, flux tubes, local edge ray,differential evolution, or orthogonal descent each respectivelyoperating on ray density locations, geometry gradient importance areasor merit function variable matrix discovery, and then ray-tracing againto verify that the perturbation has worked.

In another embodiment of the present technology, the T-spline loft lens900-B network was subsequently optimized first through a flow-line,optical path, or flux tube approach. Although not preferred, it would beequivalent to a person skilled in the art to use differential evolutionand orthogonal descent eliminate the need for calculating derivatives ofthe merit function for arriving at the primitive T-spline optical lightcontrol network skeleton.

A person of ordinary skill in the optical design and computer modelingarts or CAD design may accommodate the optimization element 114 toaccomplish a similar result for the same purpose of scaling the meshusing different techniques. Examples of such techniques comprise, butare not limited to: Optical ray-tracing of a t-spline optical controlsurface whether it is refractive, reflective, or diffractive can lead toimprovements in optimization through iterative refinement on thelocation and number of knots. For example, in an embodiment of thepresent technology FIG. 12, bundles of rays 122 passing through theoptical control surface leave the surface with direction cosines whichare undesirable. In FIG. 12, a T-spline light control lens with raysshows several caustic inducing skew rays. The behavior of the exitingwavefronts can be described in any number of ways. In non-imaging opticsthe merit function will likely be described by, but are not limited to;luminous intensity, illuminance grids, peak intensity, peak illuminance,encircled energy, efficiency of radiant transfer and luminance.

In the disclosed technology, the optical lens design of FIG. 12 and FIG.13 served as a test case, although many sectors stand to benefitincluding the multi-disciplinary design. The disclosed technology ormanifold T-splines topology may be used when dealing with complexsystems which require extended free-form lenses, reflectors, diffractiveregions, lightpipes, lightguides, or other light control systemoperators such as efforts required for solid state lighting fixtures.The technology is also advantageous for modeling lightpipe andlightguides which does not necessarily perform lensing, or reflection inair, it guides light from one location to another. The t-splinestopology allows for refined control over the entire optical surface.Control points can be reduced by conversion of a NURBS into a T-spline.T-splines can be used to produce new loft lenses directly from aB-spline network which can then be further refined and merged to splinepatches, or T-panels as needed. Several applications such as but notlimited to, thermal fin design, propellers or wind-turbine blades,reverse engineering from laser or LIDAR scanned models (used in specialeffects) and complex industrial design will implement the disclosedtechnology. Applications requiring complex geometry topology along withany number of the new non-imaging optimization methods will be used.

The disclosed technology and the interoperability of NURBS and T-splineswill accelerate adaptation allowing for compatibility withopto-mechanical software, tooling, and manufacturing. Optimization ofT-spline lenses may also be accomplished through simplified knotaddition and deletion. As disclosed above, T-splines overcame some ofthe issues with implementing simultaneous multiple surface designmethodology when dealing with groups of lenses and reflectors, byimproving seed patch junction continuity, elimination of ripples andholes, and precisely adding local control points where required withoutexponential increase in complexity.

It will be appreciated by those skilled in the art that changes could bemade to the embodiments described above without departing from the broadinventive concept thereof. It is understood, therefore, that thistechnology is not limited to the particular embodiments disclosed, butit is intended to cover modifications within the spirit and scope of thepresent technology.

1. A method, comprising: refining geometries in at least one CAD modelby converting at least one B-spline network into a NURBS network andfurther converting said NURBS network into at least one T-splinenetwork.
 2. The method of claim 1, further comprising the adding of atleast one control point on said T-spline network.
 3. The method of claim1, further comprising the optimizing of at least one weight across saidnetwork.
 4. The method of claim 1, further comprising the merging atleast one of said NURBS surface with at least one of said T-splinesurface.
 5. The method of claim 1, wherein said network is a controlpoint lattice.
 6. The method of claim 1, wherein said network defines anoptical control point surface.
 7. The method of claim 1, wherein saidCAD model is selected from the group consisting of: optical lensdesigns, optical reflector designs, extended free form lenses,reflectors, diffractive regions, loft lenses, lightpipes, lightguides,thermal fin designs, propeller designs, and wind turbine blade designs.8. The method of claim 3, wherein the optimizing step is selected fromthe group consisting of: optical ray-tracing, scaling of blendingfunctions, flow-line method, SMS, flux tubes, local edge ray,differential evolution, orthogonal descent on ray density locations,geometry gradient, and merit function variable matrix discovery.
 9. Themethod of claim 3, wherein the optimizing step is accomplished byscaling the weights across said network in terms of its flux density.10. The method of claim 3, wherein the optimizing step is accomplishedby scaling the weights across said network in terms of its geometrygradient.
 11. A method of CAD surface interpolation comprising the stepsof: converting at least one B-spline surface into at least one NURBSsurface; converting at least one NURBS surface into at least oneT-spline surface; and merging at least one of said NURBS surface with atleast one of said T-spline surface.
 12. The method of claim 11, whereinsaid surface contains a control point lattice.
 13. The method of claim12, further comprising the adding of at least one control point on saidcontrol point lattice.
 14. The method of claim 11, further comprisingthe optimizing of at least one weight about said surface.
 15. The methodof claim 11, wherein said surface is an optical control point surface.16. The method of claim 11, wherein said CAD surface is selected fromthe group consisting of: optical lens designs, free form lenses,reflectors, diffractive regions, loft lenses, lightpipes, lightguides,thermal fin designs, propellers and wind turbine blades.
 17. The methodof claim 14, wherein the optimizing step is selected from the groupconsisting of: optical ray-tracing, scaling of blending functions,flow-line methods, SMS, flux tubes, local edge rays, differentialevolution, orthogonal descent on ray density locations, geometrygradient, and merit function variable matrix discovery.
 18. The methodof claim 14, wherein the optimizing step is accomplished by scaling theweights across said network in terms of flux density or geometrygradient.
 19. A method, comprising: refining geometries in at least oneCAD model by optimizing at least one T-spline network.
 20. The method ofclaim 19, wherein the optimizing step comprises the adding of at leastone control point on said T-spline network.
 21. The method of claim 19,wherein said network is a control point lattice.
 22. The method of claim19, wherein said network defines an optical control point surface. 23.The method of claim 19, wherein said T-spline network was previouslyconverted from at least one network selected from the group consistingof: B-splines, Powell-Sabin splines, NURBS, T-NURCC, NSS, D-NURBS andBernstein polynomials.
 24. The method of claim 19, wherein said CADmodel is selected from the group consisting of: optical lens designs,free form lenses, reflectors, diffractive regions, loft lenses,lightpipes, lightguides, thermal fin designs, propeller designs, andwind turbine blades.
 25. The method of claim 19, wherein the optimizingstep is selected from the group consisting of: optical ray-tracing,scaling of blending functions, flow-line method, SMS, flux tubes, localedge ray, differential evolution, orthogonal descent on ray densitylocations, geometry gradient, and merit function variable matrixdiscovery.
 26. The method of claim 18, wherein the optimizing step isaccomplished by scaling the weights across said network in terms of fluxdensity.
 27. The method of claim 18, wherein the optimizing step isaccomplished by scaling the weights across said network in terms ofgeometry gradient.